konuralp j. math. Konuralp Journal of Mathematics 2147-625X Mehmet Zeki SARIKAYA Applied Mathematics (Other) Uygulamalı Matematik (Diğer) Centers, Commutators, and Holomorphs of 2-Groups https://orcid.org/0000-0001-7892-6960 Aytekin Ali PAMUKKALE ÜNİVERSİTESİ https://orcid.org/0000-0002-6552-4695 Şahan Tunçar Aksaray Üniversitesi 04 30 2026 14 1 14 23 01 08 2026 03 31 2026 Copyright © 2013, Konuralp Journal of Mathematics 2013 Konuralp Journal of Mathematics

This paper explores actor structures in group-groupoids, using the Brown-Spencer theorem to establish actors as universal objects and split extension classifiers. We construct the center and commutator subgroup of a group-groupoid, revealing their roles in internal symmetries, and introduce the holomorph as a categorical generalization of the classical holomorph of a group. These results extend group-theoretic concepts to 2-groups, bridging algebra and topology. By connecting actor theory with split extensions and intrinsic algebraic properties, we provide new tools for analyzing symmetries and automorphisms in higher-dimensional algebraic structures.

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